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10 June 2012

Demonstration: Normal Force

Awesome normal force demonstration
Construction by Frank Anderson
The "normal" force is the force applied by a surface in a direction perpendicular to the surface.  It's called "normal" because, in mathematics, "normal" means "perpendicular."  The word is not being used in the sense of "typical" or "natural"; a normal force only exists when a surface is in contact with an object.

I essentially recite the above paragraph when I first introduce normal forces.  I repeat elements of the definition numerous times, as do you, I'm sure.  Yet I don't think any of us is powerful enough to prevent students calling it the "natural force," nor to stop someone from telling me that a mass hanging in the air from a string must experience a normal force so it doesn't fall to the earth.

How do I bust these misconceptions?  Repetition, and relentless hammering any time a problem set says something blatantly incorrect about a normal force.

An excellent homework problem that I made up one day, but found later in about three textbooks, says:

Describe thoroughly an example of an equilibrium situation in which:

(a) the normal force is equal to the weight of a wooden block
(b) the normal force is greater than the weight of a wooden block
(c) the normal force is less than the weight of a wooden block
(d) the normal force on a wooden block is zero

As with all physics concepts, the final key to cementing understanding is later review in context.  After a few days of equilibrium problems, I introduce equilibrium on inclined planes.  The only real difference between inclines and x-y plane problems is that the weight rather than some other force is broken up into components.  But inclines provide yet another opportunity to remind everyone of the true meaning of "normal" -- the normal force from an incline acts perpendicular to the incline, and NOT directly opposite the object's weight.

For the final inclined plane demonstration, I use the apparatus pictured above, which was constructed by my predecessor at Woodberry, Frank Anderson.  Initially, the bus of weight 2.2 N sits on a hinged wooden plank.  I set the plank at an angle of about 26 degrees.  The bus is connected to a rope that parallels the plank, over which a mass is hung.

We calculate that the string parallel to the incline must have a tension of (2.2 N)(sin 26) = 1.0 N.  Sure enough, I invite a class member to the front of the room to vouchsafe that the hanging mass over the right-hand pulley in the picture is 100 g.

Then we calculate that the normal force on the bus is (2.2 N)(cos 26) = 2.0 N.  This means the plank is pushing on the bus with 2.0 N of force.  

But what if I added a string pulling the bus perpendicular to the plank?  And what if this string had a tension of 2.0 N?  [I carefully and slowly add the 2.0 N weight over the left-hand pulley.  Unseen by the students, the bus's wheels now are barely touching the plank.]  What would happen to the normal force on the bus?  Well, the class reasons, the normal force would be zero; the string's 2.0 N would be sufficient to provide equilibrium.  And what does a normal force of zero mean?  It means no support by a surface.  

So, I ask, what's the point of the plank?  I allow the hinged plank to fall away from the bus... and the bus doesn't move.  You can see the bus's final position in the diagram above.  This never fails to induce a few "wow"s from the audience, even applause every few years.

I leave the apparatus out for a day or two after the performance.  I invariably observe some curious students fooling around with the strings and masses, trying different angles, different tensions, or just trying to reenact the demonstration I did.  


  1. I love this demonstration, too. It's also in Aaron's book "Teaching Introductory Physics."

  2. You could also put a electronic scale under the bus to show that the upward force from the plank is now 0.